Kolomeisky Research Group

THEORETICAL BIOPHYSICS & Statistical Mechanics of Complex Systems

Research overview

Our research group is working in the area of statistical mechanics of complex systems and theoretical biophysics. We are using analytical and computational tools.

Development of Morphogen Gradient Formation

The fundamental processes of biological development are governed by multiple
signaling molecules that create non-uniform concentration profiles known as morphogen
gradients. It is widely believed that the establishment of morphogen gradients is a result
of complex processes that involve diffusion and degradation of locally produced
signaling molecules. We are developing discrete-state stochastic models for
investigating the corresponding reaction-diffusion models.

Mechanisms of Motor Protein Transport

A group of catalytic proteins, known as motor proteins, such as
kinesins, dyneins, myosins, DNA and RNA polymerases operate in
biological cells by consuming energy provided by ATP hydrolysis.
They play crucial roles in cell division, cellular transport,
muscle contraction and genetic transcription. Current experimental
techniques allow measurements of biochemical and mechanical
properties of motor proteins with single-molecule precision.
However, the main fundamental question related to motor proteins
- how the chemical energy is transformed into mechanical motion -
is still unanswered. We are developing stochastic models of the
motion of motor proteins which take into consideration the
biochemical complexity of these processes. Our theoretical
methods will be used to describe existing and future experiments
on motor protein transport.

Dynamics of Surface-mounted Thioethers

Recent single-molecule experiments indicated that thioethers (dialkylsulphides) deposited on the gold surface may act as thermally or mechanically activated molecular motors, although the factors affecting the properties of such surface-mounted rotors are not yet clearly understood. In particular, it was found that for the thioethers containing up to six carbon atoms in each chain the rotational energy barriers are almost independent on the alkyl chain length with the only exception of the dimethylsulphide for which the rotation is almost barierless. This observation contradicts the naive assumption that the rotation activation energies should increase with the increase of the molecule size. We use molecular dynamics simulations to study the dynamics of thioethers and other surface-mounted rotors.

Dynamics of Polymer Translocation across Nanopores

The transfer of DNA, RNA and proteins through cell membranes is fundamental to the understanding of multiple biological processes.
The transport of linear polymer molecules across the nanopores is also important in many chemical and industrial processes. However, our
theoretical understanding of these complex phenomena is still very limited. Experiments suggest that the dynamics of translocation strongly
depends on the size, flexibility, and chemical and electrostatic interactions between the polymers and the pores. We are developing theoretical models
which explicitly take into account these properties.

Microtubules and actin filaments are rigid cylindrical biopolymers which are important in cell division, in internal organization of cells
and in cell motility. It is known that the growth of microtubules and
actin filaments generate forces which determine the biological functioning
of these biopolymers. We are developing detailed models of microtubule and
actin filaments growth which take into account the complex structure and
the lateral interactions of monomers in these biopolymers. We are also
interested in explaining the dynamic instability phenomena in microtubules
and the coupling between actin filaments growth and cell membrane tension.
Our theoretical work is done in collaboration with experimental group of
Prof. W. Brownell from Baylor College of Medicine.

Thermodynamics of Electrolytes

Electrolytes play important roles in science and industry. However,
the complete thermodynamic description of these systems is still an
open question. Current experimental and theoretical studies are focused
on critical properties of ionic fluids where controversial results exist.
We are developing Debye-Huckel-based theories for lattice models of
electrolytes. Our theories are focusing on the effects of size- and
charge asymmetry of charged particles on macroscopic thermodynamic
properties. We are checking our theoretical predictions with extensive
computer simulations. In this area our collaborator is Prof.
Panagiotopoulos from Princeton University.

1D Nonequilibrium Multi-Particle Transport

Multi-particle transport phenomena are important for understanding
the mechanisms of nonequilirbrium processes in chemistry, physics and
biology (such as gel electrophoresis, kinetics of biopolymerization,
ion channels, traffic problems, polymer dynamics, surface growth,
anomalous conductivity). The complexity of these problems arises from
the nonequilibrium nature of these phenomena. We are investigating the
effects of detachments/attachments, inhomogeneity, chemical processes
and particles size on transport properties of interacting particles.
These problems are studied by the means of exact analysis, mean-field
theories and Monte Carlo simulations.

Theory of Biocrystallization Processes

Recently, we started a new project on theoretical modeling of
biocrystallization processes, mainly protein crystallization. The range
of molecule-molecule interactions in proteins, (in contrast to simple
compounds like water, nitrogen, etc.) is much smaller than the size of
the molecules. This leads to a complex dynamics of crystallization,
which is not well understood theoretically. We are developing simple
models of protein crystallization which take into account the intermediate
states and phase transitions. Our theoretical efforts are accompanied by
experimental work with Prof. P. Vekilov from University of Houston.

Protein-DNA Interaction

Protein searching and recognizing the targets on DNA was the subject of many experimental and theoretical
studies. It is often argued that some proteins are capable of finding their targets 10-100 times faster than
predicted by the three-dimensional diffusion rate. However, recent single-molecule experiments showed that
the diffusion constants of the protein motion along DNA are usually small. This controversy pushed us to
revisit this problem. We are investigating this problem both analytically and computationally to throw some
light into the physical-chemical aspects of the target search and recognition.
Currently we are performing extensive Monte Carlo simulations.